This is for math geeks and musicians. From Scientific American:

When we tune an instrument, we would like for all our octaves and fifths to be perfect. One way to tune an instrument would be to start with a pitch and start working out the fifths above and below it it. We start with some frequency that we call C. Then 3/2 times that frequency is G, 9/4 times that frequency is D (an octave and a step above our original C), and so on. If you learned about the “circle of fifths” at some point in your musical life, then you know that if we keep going up by fifths, we’ll eventually land back on something we’d like to call C.

The same is true with circle of fourths. You should, logically, end up where you started, albeit an integer number of octaves higher or lower. But sadly, the math doesn’t work, and you end up tweaking those tunings to create perfect octaves. Read the article to follow the math. It’s enlightening.